CAIE A-Level Mathematics 3.9.5 Complex numbers

CAIE A-Level Mathematics 3.9.5 Complex numbers
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise multiplying, dividing and powering complex numbers in polar or exponential form, tracking exact moduli and arguments.

How this is tested

  • combine moduli and arguments to express products or quotients as re^{iθ}

Question 3(a)

[Maximum number: 2]

The complex numbers s and t are given by

s=5(cos⁡0.25+isin⁡0.25) and t=6e3is=5(\cos 0.25+\mathrm{i} \sin 0.25) \quad \text { and } \quad t=6 \mathrm{e}^{3 \mathrm{i}}

Express st\frac{s}{t} in the form reiθr \mathrm{e}^{\mathrm{i} \theta}, where −π<θ⩽π-\pi<\theta \leqslant \pi and r>0.